Download DEPARTMENT OF MATHEMATICS COURSE INFORMATION

DEPARTMENT OF MATHEMATICS
COURSE INFORMATION SHEET FOR
MAT204 – COLLEGE ALGEBRA WITH
TRIGONOMETRY II
All members of the Math Department at Clinton Community College use the respective course
templates as a basis for their course syllabi. Faculty may, at their discretion, change the order
of the course content or add course content.
COURSE NUMBER AND TITLE: MAT204 - College Algebra with Trigonometry II
COURSE SECTION: TBA
CONTACT HOURS: 4
CREDIT HOURS: 4
SEMESTER AND YEAR: TBA
INSTRUCTOR’S NAME, TELEPHONE NUMBER, EMAIL ADDRESS, OFFICE
NUMBER, AND OFFICE HOURS: TBA
I. COURSE DESCRIPTION:
This course is the second of a two-semester sequence designed to prepare students for calculus
and technical courses. Course topics include exponential, logarithmic, and trigonometric
functions; trigonometric identities and equations; oblique triangles; polar coordinates; conic
sections; systems of equations; and matrices. The use of the graphing calculator is required for
this course to further the exploration of these topics and their applications.
III. PREREQUISITE: MAT104-College Algebra with Trigonometry I or equivalent
III. COURSE OBJECTIVES, SUNY GENERAL EDUCATION KNOWLEDGE AREA
LEARNING OUTCOMES AND ASSESSMENT:
COURSE OBJECTIVES:
As the result of instructional activities, students will be able to:
1. Form a composite function.
2. Determine whether a function is one-to-one.
3. Find the inverse of a one-to-one function graphically and algebraically.
4. Graph exponential and logarithmic functions and identify their domain and range.
5. Convert exponential expressions to logarithmic, and vice versa.
6. Use the properties of logarithms to simplify or expand logarithmic expressions.
7. Solve exponential and logarithmic equations.
8. Solve applications of exponential growth, exponential decay, logarithmic, and logistic
functions.
revised 8/11
9. Use the graphing calculator to find an exponential, logarithmic, or logistic regression
equation to model data, where appropriate.
10. Convert from radians to degrees, and vice versa.
11. Use right triangle trigonometry to solve applications.
12. Find the six trigonometric functions of any angle.
13. Determine the amplitude, period, domain and range of sine and cosine functions.
14. Graph sine and cosine curves by hand.
15. Determine the domain, range, and asymptotes of the tangent function.
16. Use the graphing calculator to find a sinusoidal regression equation to model real-life
data.
17. Use the inverse trigonometric functions to determine an angle.
18. Use trigonometric identities to simplify trigonometric expressions.
19. Prove basic trigonometric identities.
20. Use the sum and difference formulas to find exact values.
21. Use the double and half-angle formulas to find exact values.
22. Solve trigonometric equations involving a single trigonometric function algebraically and
graphically.
23. Solve trigonometric equations using identities.
24. Solve oblique triangles using the law of sines (SAA, ASA, SSA).
25. Solve oblique triangles using the law of cosines (SAS, SSS).
26. Solve applications of oblique triangles.
27. Plot points using polar coordinates.
28. Convert from polar coordinates to rectangular coordinates and vice versa.
29. Find the vertex, focus, and directrix of a parabola and graph it.
30. Find the center, major axis, foci, and vertices of an ellipse and graph it.
31. Find the center, transverse axis, vertices, and foci of a hyperbola and graph it.
32. Identify a conic given its equation.
33. Use a rotation of axes to transform equations.
34. Solve a system of linear equations in two variables by substitution or elimination.
35. Identify a system as consistent or inconsistent and its equations as dependent or
independent.
36. Solve systems of three equations in three variables algebraically.
37. Solve systems of linear equations using matrices.
38. Find the sum and difference of two matrices.
39. Find scalar multiples of a matrix.
40. Find the product of two matrices.
41. Find the inverse of a matrix.
42. Solve systems of equations using an inverse matrix.
43. Solve systems of nonlinear equations algebraically and graphically.
revised 8/11
SUNY GENERAL EDUCATION KNOWLEDGE AREA COMPETENCIES:
Students will demonstrate the ability to:
1. interpret and draw inferences from mathematical models such as formulas, graphs, tables
and schematics;
2. represent mathematical information symbolically, visually, numerically and verbally;
3. use arithmetical, algebraic, geometric and statistical methods to solve problems;
4. estimate and check mathematical results for reasonableness, determine alternatives and
select optimal results; and
5. recognize the limits of mathematical and statistical methods.
IV. REQUIRED TEXTBOOK AND MATERIALS:
REQUIRED TEXTBOOK:
Algebra and Trigonometry w/MyMathLab, 9th edition; Sullivan. Prentice Hall.
ISBN #978-0-321-76065-4
REQUIRED MATERIALS:
A graphing calculator (the TI-83, TI-83 Plus, or TI-84 Plus are strongly recommended)
V. METHODS OF INSTRUCTION/COURSE ORGANIZATION: To be determined by the
respective instructor.
VI. ATTENDANCE PROCEDURE (INCLUDING MAKEUP POLICY): To be determined
by the respective instructor.
VII. BIBLIOGRAPHY OF READINGS (IF APPLICABLE): To be determined by the
respective instructor.
VIII. METHODS OF EVALUATION (INCLUDING THE CALCULATION OF COURSE
GRADE): To be determined by the respective instructor. The methods of evaluation shall
include tests (test types, length and weight of each), papers (weight of each), projects (weight of
each), and other forms of evaluation (weight of each).
IX. GRADING SCALE: To be determined by the respective instructor. The grading scale shall
indicate what numerical scores correspond to the following grades: A, A-, B+, B, B-, C+, C, C-,
D+, D, and F.
Please Include: If you have, or suspect you may have, any type of disability or learning problem
that may require extra assistance or special accommodations, please speak to me privately after
class or during my office hours as soon as possible so I can help you obtain any assistance you
may need to successfully complete this course. You should also contact Laurie Bethka, Room
420M in the Academic Assistance Center, for further assistance.
revised 8/11
X. GENERAL TOPICS OUTLINE:
1.
Exponential and Logarithmic Functions (textbook chapter 6)
including composition of functions, inverse functions, definitions and graphs of
exponential and logarithmic functions, properties of logarithms, solving equations
and applications
2.
Trigonometric Functions (textbook chapter 7)
including radian and degree measure, right triangle trigonometry, the unit circle,
graphs of trigonometric functions, sinusoidal regression
3.
Analytic Trigonometry (textbook chapter 8)
including inverse trig functions, fundamental identities, solving trigonometric
equations
4.
Applications of Trigonometry (textbook chapter 9, 10.1)
including laws of sines and cosines, polar coordinates
5.
Analytic Geometry (textbook chapter 11)
including circles and ellipses, parabolas, hyperbolas, and rotation of axes
6.
Systems of Equations and Matrices (textbook chapter 12)
including solving systems of linear equations: substitution, elimination, and
matrices; matrix algebra; systems of nonlinear equations
XI. ACADEMIC INTEGRITY: Academic honesty is expected of all Clinton Community
College students. It is academically dishonest, for example, to misrepresent another person’s
work as one’s own, to take credit for someone else’s work or ideas, to accept help on a test, to
obtain advanced information on confidential test materials, or to intentionally harm another
student’s chances for academic success.
XII. COURSE CONTINUITY PLAN: In the case that the college officially closes because of
an emergency which causes a short term disruption of this course, we will utilize e-mail to
continue this course in the short term (1-3 weeks). All students need to utilize their campus
e-mail to receive course related information.
revised 8/11